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Given relation R is the set Z of all integers is given by \( R= \{(a,b) \in Z \times Z, a-b\) is an integer }. Find whether R is an equivalence relation or not.
cbse
class12
modelpaper
2012
sec-b
q11
math
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asked
Feb 2, 2013
by
thanvigandhi_1
edited
Jul 25, 2013
by
sreemathi.v
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Given relation R in the set Z of all integers is given by \( R = {(a,b) \in Z * Z\: a-b \: is\: an\: integer }\). Find whether R is an equivalence relation or not.
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Show that the relation R in the set \( A = { x \in Z:0 \leq x \leq 12},\) given by (i) R = { a, b : |a-b| is a multiple of 4 } (ii) R = {a, b ; a = b}. is equivalence relation. Find the set of all eleents related to 1 in each case.
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Jan 10, 2013
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Let R be the relation defined in the set A = {1, 2, 3, 4, 5, 6, 7} by R = {(a, b): both a and b are either odd or even}. Show that R is an equivalence relation. Further, show that all the elements of the subset{1, 3, 5, 7} are related to each other and all elements of the subset {2, 4, 6} are related to each other, but no element of the subset {1, 3, 5, 7}} is related to any element of the subset {2, 4, 6}.
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Jan 23, 2013
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Show that the relation R in the set A = {1, 2, 3, 4, 5} is given by R = {(a, b) : |a-b|is even }, is an equivalence relation. Show that all the elements of {1, 3, 5} are related to each other and all the elements of {2, 4} are related to each other. But no element of {1, 3, 5} is related to any element of {2, 4}.
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Jan 4, 2013
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Feb 15, 2013
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Show that the relation R in the set A of points, given by R: {P, Q): distance of the point P from the origin is the same as the distance of Q from the origin }, is an equivalence relation. Further, show that the set of all points related to P = (0, 0) is the circle passing through P with origin as the centre.
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Jan 8, 2013
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cbse
class12
modelpaper
2012
sec-b
q11
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